What is the test for an Eighth Amendment claim arising out of inadequate medical care?

To "establish an Eighth Amendment claim arising out of inadequate medical care, a prisoner must prove deliberate indifference to his serious medical needs." Chance v. Armstrong, 143 F.3d 698, 702 (2d Cir. 1998) (internal quotation marks and brackets omitted). Deliberate indifference has objective and subjective components: "First, the alleged deprivation must be, in objective terms, sufficiently serious. Second, the defendant must act with a sufficiently culpable state of mind." Id. (internal quotation marks and citation omitted). To satisfy the subjective component, a plaintiff must establish "that the charged official act[ed] or fail[ed] to act while actually aware of a substantial risk that serious inmate harm will result." Salahuddin v. Goord,

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